Projection lens and projection television system using the same

ABSTRACT

A projection lens for projecting images displayed on an image display device having angle-of-view dependency has high image focusing characteristics corresponding to high definition images, wide field angle, and telecentric characteristics. In addition, a projection television system using the same can be minimized in its size.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a projection television system in which images formed, by means of electric signals as a result of changes of transmittance and reflectivity of the light, on an image display element are magnified and projected on a screen, and to projection lens preferable to be used therein.

2. Description of the Prior Art

There has been a projection television system as the display devices with large image planes. The CRT type projection television systems in which images of high brightness on the CRT are projected on the screen by means of the projection lens have been already used practically. On the other hand, a liquid crystal type projection television system in which images on a liquid crystal display element forming the images by changing transmittance and reflectivity of the light by means of video signals are magnified and projected on a screen are starting to be developed.

In the case of projecting images on the liquid crystal display element, there occur problems, which are free from the CRT projection, as described below:

(1) Considering the angle-of-view dependency of the liquid crystal display element, a bundle of rays radiated in a specific range of angle toward the liquid crystal display element has to be utilized as a projection bundle of rays in order to project the images, which are formed on the liquid crystal display element according to the video signals, on the screen with high contrast. Therefore, the projection lens are required to have telecentric characteristics that off-axis principal rays become vertical to the liquid crystal display element.

(2) The liquid crystal display element is driven by matrix electrodes, so that it is difficult to electrically compensate picture distortion of the projected images not like the projection system using the CRT devices. Accordingly, the distortion aberration of the projection lens must be as small as possible.

These problems generally become a large obstacle to realize the wide picture angle of the projection lens which is necessary to minimize the size of the projection television system. These problems are not only against the liquid crystal display element but also against other image display elements which forms the images as a result of changes of transmittance and reflectivity of the light by means of video signals using biretringence or rotatory polarization characteristics such as electric optical crystal and PLZT or the like having angle-of-view dependency.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a projection television system with high performance and a lens preferable to be used therein having low distortion aberration and capability to project the images on an image display element having angle-of-view dependency forming the images as changes of transmittance and reflectivity of the light by means of the electric signals in order to solve the above problems which occur due to the difference from the image projection of the CRT in case of projecting the images on the image display element having the angle-of-view dependency.

In order to achieve the above object, the projection television system of the present invention comprises: a light source; an image display element having angle-of-view dependency forming images as changes of transmittance or reflectivity by means of image electric signals; a projection lens magnifyingly projecting a bundle of image rays achieved by transmitting the rays through said image display element or by reflecting the rays against said image display element, wherein said projection lens is provided so as to make off-axis principal rays substantially vertical to said image display element and has predetermined telecentric characteristics in order to obtain projection images with high contrast. It is desirable for the projection lens to have a wide field angle particularly in order to achieve a compact transmission type projection television system. Accordingly, the projection lens has a constitution that an inverted telephoto type front lens group and a rear lens group having a front focal point nearby an exit pupil of said front lens group are provided.

According to the above constitution, the wide field angle can be achieved because the front group is made of the inverted telephoto type lens, and the telecentric characteristics can be obtained by arranging the rear lens group having a front focal point nearby the exit pupil of said front lens group, so that the images on the image display element having angle-of-view characteristics can by magnifyingly projected on the screen with high contrast.

As described above, according to the present invention, an excellent image with high contrast can be displayed, especially, a transmission type projection television system corresponding to the high definition of the images can be realized, and it is of great value in industry.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view showing the configuration of a projection lens of a first embodiment.

FIGS. 2 (a), (b) and (c) to 11 (a), (b) and (c) are characteristics graphs of spherical aberration, astigmatism aberration, and distortion aberration of the first to tenth embodiments.

FIG. 12 is a diagram of a transmission type projection television set using a light source, a reflection type liquid crystal element as an image display element having angle-of-view dependency, and a projection lens having telecentric characteristics.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention is described hereinafter referring to the drawings.

FIG. 1 is a view showing a schematic configuration of a projection television system, in which the projection lens of a first embodiment of the present invention is employed, using a reflection type liquid crystal display element as an image display element having angle-of-view dependency. In FIG. 1, projection lens 3 constituted of a front lens group 1 and a rear lens group 2 having a front focal point nearby an exit pupil of said front lens group 1, a polarizing beam splitter 4, and a reflection type liquid crystal display element 5 are shown respectively. Light rays radiated from a light source 9 through an upper portion of the polarizing beam splitter 4 are refracted toward the reflection type liquid crystal display element 5 by means of the polarizing beam splitter 4, and enter into the reflection type liquid crystal display element 5. The light intensity-modulated according to images on the reflection type liquid crystal display element 5, then travels through the polarizing beam splitter 4 and projects magnified images of the reflection type liquid crystal display element 5 on a screen by means of the projection lens 3.

The projection lens 3 includes the front lens group 1 and the rear lens group 2 which are constituted by 7 lens pieces and 3 lens pieces respectively. Namely, starting from the screen side, a first lens is a positive lens, a second lens is a negative meniscus lens having its convex surface facing the screen side, a third lens is a negative meniscus having its convex surface facing the screen side, a fourth lens is a bi-convex lens, a fifth lens is a negative meniscus lens including a cemented surface and having its convex surface facing the screen surface, a sixth lens is a positive meniscus lens having its concave surface facing the screen side, a seventh lens is a bi-convex lens, an eight lens is a bi-concave lens, a ninth lens is a positive lens, and a tenth lens is a bi-convex lens. As described above, the first to seventh lens form the front lens group 1 of the inverted telephoto type lens constitution, and the eighth to tenth lens form the rear lens group 2 having the front focal point nearby the exit pupil of the front lens group 1. By means of this constitution, realized are the telecentric characteristics which are required conditions for projecting the images on the reflection type liquid crystal display element with high contrast, and the aberrations such as the distortion aberration are compensated excellently.

In order to achieve these characteristics, it is desirable to meet the following condition.

    0.8<f.sub.1,7 /f<1.4                                       (1)

f: a total focal length of the entire system f₁,7 : a total focal length of the first to seventh lens

The condition (1) defines power distribution of the front lens group 1 toward the entire system. It becomes difficult to meet a predetermined back focus when it goes beyond a lower limit. When it goes beyond an upper limit, the rear lens group has to have excessively large power, so that it becomes difficult to compensate the aberrations, especially the distortion and coma aberrations while keeping the telecentric characteristics.

More desirably, its characteristics improve more by meeting the following condition.

    0.5<d.sub.15 /f<0.9                                        (2)

f: a total focal length of the entire system d₁₅ : a distance between surfaces of the seventh and eighth lens

The condition (2) defines the distance between the surfaces of the front and rear lens groups 1 and 2. When it goes beyond a lower limit, the power of each lens becomes large in order to maintain the telecentric characteristics, and for the purpose of realizing the telecentric characteristics a symmetric property of the power is destroyed to an even greater extent while the power is originally in an asymmetric arrangement, so that it becomes difficult especially to compensate a lateral chaotic aberration. When it goes beyond an upper limit, it is easier to achieve the telecentric characteristics, but it becomes difficult to meet a predetermined back focus.

It is much more desirable to meet the following conditions, and thus its characteristics improve even more.

    d.sub.17 /f<0.3                                            (3)

    -1.5<f.sub.8 /f.sub.9,10 <-1.2                             (4)

f: a total focal length of the entire system

d₁₇ : a distance between surfaces of the eighth and ninth lens

f₈ : a focal length of the eighth lens

f₉,10 : a total focal length of the ninth and tenth lens

The conditions (3) and (4) relate particularly to the characteristics of the eighth to tenth lens, namely of the rear lens group 2. When it goes beyond an upper limit of the condition (3), effective diameters of the ninth and tenth lens become large, so that a problem over a required cost comes about. When it goes beyond a lower limit of the condition (4), a Petzval's sum becomes large, so that it becomes difficult to compensate curvature of field. When it goes beyond an upper limit of the condition (4), the distortion aberration easily occurs, so that it becomes difficult to compensate especially circumferences of image angles. In addition, it becomes difficult to compensate outer comas.

To introduce aspheric surface increases degree of freedom on aberration compensation and can realize more excellent image forming characteristics. In the projection lens of the present invention, the compensation of the distortion aberration in particular improves by introducing an aspheric surface into at least one of the first, second, eighth, ninth and tenth lenses. In addition, the aspheric surface can be easily formed, manufacturing costs can decrease, and the lens can have a lighter weight by forming the lens group having large diameters, such as the first and second lens, using plastics.

Each embodiment of the projection lens of the present invention is shown below. In each embodiment, r₁, r₂, . . . represent a radius of curvature of each surface starting from the screen side, d₁, d₂, . . . represent a distance between each of said surfaces, n₁, n₂, . . . represent a refractive index at an e-line of each lens, ν₁, ν₂, . . . represent a Abbe's number corresponding to the e-line of each of the above lens, surfaces represented by * are the aspheric surfaces. If Z is supposed a displacement amount from a vertex of a lens at a position away from an optical axis of the lens in a radius distance Y of an opening, it can be expressed as ##EQU1## AD, AE, AF, and AG are aspherical coefficients, and K is a conical constant.

    ______________________________________                                         First embodiment                                                               ______________________________________                                         f = 49.86           Aperture 1:2.8                                                                 ratio                                                      Projection 16.89    ω = 36.2°                                     magnification                                                                  f.sub.1.7 /f = 1.08 d.sub.15 /f = 0.72                                         d.sub.17 /f = 0.12  f.sub.8 /f.sub.9.10 = -1.42                                 r.sub.1 = 136.783                                                                          d.sub.1 = 8.10                                                                           n.sub.1  = 1.51825                                                                        ν.sub.1  = 63.8                            r.sub.2  = 961.173                                                                         d.sub.2 = 5.18                                                     r.sub.3  = 69.975                                                                          d.sub.3 = 6.00                                                                           n.sub.2  = 1.51825                                                                        ν.sub.2  = 63.8                            r.sub.4  = 27.036                                                                          d.sub.4 = 8.97                                                     r.sub.5  = 121.495                                                                         d.sub.5 = 2.21                                                                           n.sub.3  = 1.52555                                                                        ν.sub.3  = 50.5                            r.sub.6 = 29.715                                                                           d.sub.6 = 18.76                                                    r.sub.7 = 74.902                                                                           d.sub.7 = 17.33                                                                          n.sub.4 =  1.85503                                                                        ν.sub.4 = 23.7                             r.sub.8 = -372.104                                                                         d.sub.8 = 6.68                                                     r.sub.9 = 271.686                                                                          d.sub.9 = 17.77                                                                          n.sub.5 = 1.79013                                                                         ν.sub.5 = 43.9                            r.sub.10 = -25.786                                                                         d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                         ν.sub.6 = 27.3                            r.sub.11 = 74.081                                                                          d.sub.11 = 4.62                                                    r.sub.12 = -81.511                                                                         d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                         ν.sub.7 = 49.4                            r.sub.13 = -43.199                                                                         d.sub.13 = 1.49                                                    r.sub.14 = 204.097                                                                         d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                         ν.sub.8 = 47.1                            r.sub.15 = -122.218                                                                        d.sub.15 = 35.89                                                   r.sub.16 = -68.864                                                                         d.sub.16 = 2.66                                                                           n.sub.9 = 1.61075                                                                         ν.sub.9 = 40.0                            r.sub.17  = 275.832                                                                        d.sub.17 = 6.11                                                    r.sub.18 = -1075.96                                                                        d.sub.18 = 10.52                                                                         n.sub.10 = 1.68083                                                                         ν.sub.10 = 55.1                           r.sub.19 = -88.713                                                                         d.sub.19 = 0.25                                                    r.sub.20 = 128.275                                                                         d.sub.20 = 10.01                                                                         n.sub.11 = 1.7762                                                                          ν.sub.11 = 49.4                           r.sub.21 = -276.533                                                                        d.sub.21 = 4.70                                                    r.sub.22 = 0.000                                                                           d.sub.22 = 41.10                                                                         n.sub.12 = 1.51825                                                                         ν.sub.12 = 63.8                           r.sub.23 = 0.000                                                               ______________________________________                                    

    ______________________________________                                         Second embodiment                                                              ______________________________________                                         f = 49.82           Aperture 1:2.8                                                                 ratio                                                      Projection 16.94    ω = 36.2°                                     magnification                                                                  f.sub.1.7 /f = 1.05 d.sub.15 /f = 0.74                                         d.sub.1.7 /f = 0.16 f.sub.8 /f.sub.9.10 = -1.33                                 r.sub.1 = 104.034                                                                        d.sub.1 = 11.00                                                                          n.sub.1 = 1.49384                                                                          ν.sub.1 = 57.4                                                                     *                                       r.sub.2 = 466.780                                                                        d.sub.2 = 5.00               *                                       r.sub.3 = 73.295                                                                         d.sub.3 = 2.00                                                                           n.sub.2 = 1.49384                                                                          ν.sub.2 = 57.4                                                                     *                                       r.sub.4 = 26.295                                                                         d.sub.4 = 11.00              *                                       r.sub.5 = 121.495                                                                        d.sub.5 = 2.21                                                                           n.sub.3 = 1.52555                                                                          ν.sub.3 = 50.5                              r.sub.6 = 29.715                                                                         d.sub.6 = 18.76                                                      r.sub.7 =  74.902                                                                        d.sub.7 = 17.33                                                                          n.sub.4 = 1.85503                                                                          ν.sub.4 = 23.7                              r.sub.8 = -372.104                                                                       d.sub.8 = 6.68                                                       r.sub.9 = 271.686                                                                        d.sub.9 = 17.77                                                                          n.sub.5 = 1.79013                                                                          ν.sub.5 = 43.9                             r.sub.10 = -25.786                                                                       d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                          ν.sub.6 = 27.3                             r.sub.11 = 74.081                                                                        d.sub.11 = 4.62                                                      r.sub.12 = -81.511                                                                       d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                          ν.sub.7 = 49.4                             r.sub.13 = -43.199                                                                       d.sub.13 = 1.49                                                      r.sub.14 = 204.097                                                                       d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                          ν.sub.8 = 47.1                             r.sub.15 = -122.218                                                                      d.sub.15 = 35.89                                                     r.sub.16 = -62.109                                                                       d.sub.16 =  2.66                                                                          n.sub.9 = 1.61075                                                                          ν.sub.9 = 40.0                             r.sub.17 = 213.114                                                                       d.sub.17 = 7.80                                                      r.sub.18 = 847.406                                                                       d.sub.18 = 10.30                                                                         n.sub.10 = 1.68083                                                                         ν.sub.10 = 55.1                             r.sub.19 = -95.951                                                                       d.sub.19 = 0.63                                                      r.sub.20 = 121.641                                                                       d.sub.20 = 10.45                                                                         n.sub.11 = 1.77622                                                                         ν.sub.11 = 49.4                             r.sub.21 = -255.505                                                                      d.sub.21 = 4.50                                                      r.sub.22 = 0.000                                                                         d.sub.22 = 41.10                                                                         n.sub.12 = 1.51825                                                                         ν.sub.12 = 63.8                             r.sub.23 = 0.000                                                               ______________________________________                                         Aspheric coefficient                                                           ______________________________________                                         First surface:                                                                  K = 0.655275     AD = 0.626082 × 10.sup.-7                              AE = -0.144786 × 10.sup.-10                                                                AF = -0.109334 × 10.sup.-14                            Second surface:                                                                 K = 0.367907 × 10.sup.2                                                 Third surface:                                                                  K = 0.440304     AD = 0.126898 × 10.sup.-7                              AE = 0.634832 × 10.sup.-11                                                                 AF = 0.928375 × 10.sup.-14                             Fourth surface:                                                                 K = -0.241861 × 10.sup.-1                                                                 AD = 0.166124 × 10.sup.-6                              AE = 0.434466 × 10.sup.-9                                                                  AF = 0.561828 × 10.sup.-12                             ______________________________________                                    

    ______________________________________                                         Third embodiment                                                               ______________________________________                                         f = 52.47           Aperture 1:2.8                                                                 ratio                                                      Projection 17.19    ω = 33.8°                                     magnification                                                                  f.sub.1.7 /f = 1.09 d.sub.15 /f = 0.64                                         d.sub.17 /f = 0.12  f.sub.8 /f.sub.9.10 = -1.31                                 r.sub.1 = 148.519                                                                         d.sub.1 = 8.40                                                                           n.sub.1 = 1.51825                                                                         ν.sub.1 = 63.8                                                                     *                                       r.sub.2 = -6939.731                                                                       d.sub.2 = 5.18                                                      r.sub.3 = 49.137                                                                          d.sub.3 = 6.00                                                                           n.sub.2 = 1.51825                                                                         ν.sub.2 = 63.8                              r.sub.4 = 29.177                                                                          d.sub.4 = 9.37              *                                       r.sub.5 = 608.860                                                                         d.sub.5 = 2.21                                                                           n.sub.3 = 1.52555                                                                         ν.sub.3 = 50.5                              r.sub.6 = 28.525                                                                          d.sub.6 = 18.76                                                     r.sub.7 = 74.902                                                                          d.sub. 7 = 17.33                                                                         n.sub.4 = 1.85503                                                                         ν.sub.4 = 23.7                              r.sub.8 = -372.104                                                                        d.sub.8 = 6.68                                                      r.sub.9 = 271.686                                                                         d.sub.9 = 17.77                                                                          n.sub.5 = 1.79013                                                                         ν.sub.5 = 43.9                             r.sub.10 = -25.786                                                                        d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                         ν.sub.6 = 27.3                             r.sub.11 = 74.081                                                                         d.sub.11 = 4.62                                                     r.sub.12 = -81.511                                                                        d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                         ν.sub.7 = 49.4                             r.sub.13 = -43.199                                                                        d.sub.13 = 1.49                                                     r.sub.14 = 204.097                                                                        d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                         ν.sub.8 = 47.1                             r.sub.15 = -122.218                                                                       d.sub.15 = 33.60                                                    r.sub.16 = -49.674                                                                        d.sub.16 = 2.66                                                                           n.sub. 9 = 1.62059                                                                        ν.sub.9 = 36.4                             r.sub.17 = 298.959                                                                        d.sub.17 = 6.11              *                                      r.sub.18 = -275.028                                                                       d.sub.18 = 10.70                                                                         n.sub.10 = 1.68083                                                                        ν.sub.10 = 55.1                                                                     *                                      r.sub.19 = -56.037                                                                        d.sub.19 = 0.25                                                     r.sub.20 = 341.327                                                                        d.sub.20 = 11.05                                                                         n.sub.11 = 1.77622                                                                        ν.sub.11 = 49.4                                                                     *                                      r.sub.21 = -103.830                                                                       d.sub.21 = 6.70                                                     r.sub.22 = 0.000                                                                          d.sub.22 = 43.30                                                                         n.sub.12 = 1.51825                                                                        ν.sub.12 = 63.8                             r.sub.23 = 0.000                                                               ______________________________________                                         Aspheric coefficient                                                           ______________________________________                                         First surface:                                                                  K = -0.2749912 × 10.sup.-1                                                                AD = 0.2548179 × 10.sup.-7                             AE = -0.2056712 × 10.sup.-10                                                               AF = -0.4319405 × 10.sup.-14                           AG = 0.8811238 × 10.sup.-18                                              Fourth surface:                                                                 K = 0.3668809 × 10.sup.-1                                                                 AD = 0.1536691 × 10.sup.-6                             AE = -0.1142634 × 10.sup.-10                                                               AF = 0.8573753 × 10.sup.-12                            AG = 0.2158643 × 10.sup.-15                                              Seventeenth surface:                                                            K = 0.2637872 × 10.sup.2                                                                  AD = 0.1858271 × 10.sup.-6                             AE = 0.1334531 × 10.sup.-10                                                                AF = 0.2612238 × 10.sup.-13                            AG = 0.9178511 × 10.sup.-17                                              Eighteenth surface:                                                             K = 0.5903051 × 10.sup.1                                                                  AD = -0.2472130 × 10.sup.-6                            AE = 0.1460313 × 10.sup.-9                                                                 AF = 0.3400976 × 10.sup.-13                            AG = 0.3706282 × 10.sup.-17                                              Twentieth surface:                                                              K = -0.9201606   AD = -0.1022347 × 10.sup.-6                            AE = 0.7465995 × 10.sup.-10                                                                AF = 0.1567219 × 10.sup.-13                            AG = 0.1032802 × 10.sup. -17                                             ______________________________________                                    

    ______________________________________                                         Fourth embodiment                                                              ______________________________________                                         f = 49.94           Aperture 1:2.8                                                                 ratio                                                      Projection 18.09    ω = 34.1°                                     magnification                                                                  f.sub.1.7 /f = 1.14 d.sub.15 /f = 0.67                                         d.sub.17 /f = 0.12  f.sub.8 /f.sub.9.10 = -1.37                                 r.sub.1 = 146.163                                                                         d.sub.1 = 8.40                                                                           n.sub.1 = 1.51825                                                                         ν.sub.1 = 63.8                                                                     *                                       r.sub.2 = 0.000                                                                           d.sub.2 = 5.18                                                      r.sub.3 = 49.670                                                                          d.sub.3 = 6.00                                                                           n.sub.2 = 1.51825                                                                         ν.sub.2 = 63.8                              r.sub.4 = 29.101                                                                          d.sub.4 = 9.39              *                                       r.sub.5 = 937.536                                                                         d.sub.5 = 2.21                                                                           n.sub.3 = 1.52555                                                                         ν.sub.3 = 50.5                              r.sub.6 = 28.141                                                                          d.sub.6 = 18.76                                                     r.sub.7 = 74.902                                                                          d.sub.7  = 17.33                                                                         n.sub.4 = 1.85503                                                                         ν.sub.4 = 23.7                              r.sub.8 = -372.104                                                                        d.sub.8 = 6.68                                                      r.sub.9 = 271.686                                                                         d.sub.9 = 17.77                                                                          n.sub.5 = 1.79013                                                                         ν.sub.5 = 43.9                             r.sub.10 = -25.786                                                                        d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                         ν.sub.6 = 27.3                             r.sub. 11 = 74.081                                                                        d.sub.11 = 4.62                                                     r.sub. 12 = -81.511                                                                       d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                         ν.sub.7 = 49.4                             r.sub. 13 = -43.199                                                                       d.sub.13 = 1.49                                                     r.sub. 14 = 204.097                                                                       d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                         ν.sub.8 = 47.1                             r.sub. 15 = -122.218                                                                      d.sub.15 = 33.60                                                    r.sub. 16 =  -49.674                                                                      d.sub.16 = 2.66                                                                           n.sub.9 = 1.62059                                                                         ν.sub.9 = 36.4                             r.sub. 17 = 303.305                                                                       d.sub.17 = 6.11              *                                      r.sub. 18 = -310.381                                                                      d.sub.18 = 10.70                                                                         n.sub.10 = 1.68083                                                                        ν.sub.10 = 55.1                                                                     *                                      r.sub. 19 = -54.486                                                                       d.sub.19 = 0.25                                                     r.sub. 20 = 275.356                                                                       d.sub.20 = 11.05                                                                         n.sub.11 = 1.77622                                                                        ν.sub.11 = 49.4                                                                     *                                      r.sub. 21 = -108.456                                                                      d.sub.21 = 6.70                                                     r.sub. 22 = 0.000                                                                         d.sub.22 = 43.30                                                                         n.sub.12 = 1.51825                                                                        ν.sub.12 = 63.8                             r.sub. 23 = 0.000                                                              ______________________________________                                         Aspheric coefficient                                                           ______________________________________                                         First surface:                                                                 K = -0.2301050 × 10.sup.-1                                                                 AD = 0.2511178 × 10.sup.-7                             AE = -0.1943356 ×  10.sup.-10                                                              AF = -0.3619595 × 10.sup.-14                           AG = 0.8095271 × 10.sup.-18                                              Fourth surface:                                                                 K = 0.3295092 × 10.sup.-1                                                                 AD = -0.4594244 × 10.sup.-7                            AE = 0.7461787 × 10.sup.-10                                                                AF = 0.4135199 × 10.sup.-12                            AG = -0.3071122 × 10.sup.-15                                             Seventeenth surface:                                                            K = 0.2504243 = 10.sup.2                                                                        AD = 0.1782731 × 10.sup.-6                             AE = -0.1529465 × 10.sup.-11                                                               AF = 0.2164382 × 10.sup.-13                            AG = -0.7725707 × 10.sup.-17                                             Eighteenth surface:                                                             K = 0.1032711 × 10.sup.2                                                                  AD = -0.2772488 × 10.sup.-6                            AE = 0.1544648 × 10.sup.-9                                                                 AF = 0.2193979 × 10.sup.-13                            AG = -0.1042978 × 10.sup.-16                                             Twentieth surface:                                                              K = -0.5525461 × 10.sup.1                                                                 AD = -0.1231838 × 10.sup.-6                            AE = 0.8516421 × 10.sup.-10                                                                AF = 0.1510178 × 10.sup.-13                            AG = 0.1229936 × 10.sup.-18                                              ______________________________________                                    

    ______________________________________                                         Fifth embodiment                                                               ______________________________________                                         f = 50.00           Aperture 1:2.8                                                                 ratio                                                      Projection 18.10    ω = 34.0°                                     magnification                                                                  f.sub.1.7 /f = 1.14 d.sub.15 /f = 0.67                                         d.sub.17 /f = 0.12  f.sub.8 /f.sub.9.10 = -1.35                                 r.sub.1 = 139.093                                                                         d.sub.1 = 8.40                                                                           n.sub.1 = 1.51825                                                                         ν.sub.1 = 63.8                                                                     *                                       r.sub.2 = 1883.809                                                                        d.sub.2 = 5.18                                                      r.sub.3 = 44.322                                                                          d.sub.3 = 6.00                                                                           n.sub.2 = 1.51825                                                                         ν.sub.2 = 63.8                              r.sub.4 = 26.610                                                                          d.sub.4 = 11.06                                                     r.sub.5 = 1031.968                                                                        d.sub.5 = 2.21                                                                           n.sub.3 = 1.52555                                                                         ν.sub.3 = 50.5                              r.sub.6 = 28.804                                                                          d.sub.6 = 18.76                                                     r.sub.7 = 74.902                                                                          d.sub.7 = 17.33                                                                          n.sub.4 = 1.85503                                                                         ν.sub.4 = 23.7                              r.sub.8 = -372.104                                                                        d.sub.8 = 6.68                                                      r.sub.9 = 271.686                                                                         d.sub.9 = 17.77                                                                          n.sub.5 = 1.79013                                                                         ν.sub.5 = 43.9                             r.sub.10 = -25.786                                                                        d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                         ν.sub.6 = 27.3                             r.sub.11 = 74.081                                                                         d.sub.11 = 4.62                                                     r.sub.12 = -81.511                                                                        d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                         ν.sub.7 = 49.4                             r.sub.13 = -43.199                                                                        d.sub.13 = 1.49                                                     r.sub.14 = 204.097                                                                        d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                         ν.sub.8 = 47.1                             r.sub.15 = -122.218                                                                       d.sub.15 = 33.60                                                    r.sub.16 = -48.652                                                                        d.sub.16 = 2.66                                                                           n.sub.9 = 1.62059                                                                         ν.sub.9 = 36.4                             r.sub.17 = 293.965                                                                        d.sub.17 = 6.11              *                                      r.sub.18 = -406.452                                                                       d.sub.18 = 10.70                                                                         n.sub.10 = 1.68083                                                                        ν.sub.10 = 55.1                                                                     *                                      r.sub.19 = -56.325                                                                        d.sub.19 = 0.25                                                     r.sub.20 = 243.391                                                                        d.sub.20 = 11.05                                                                         n.sub.11 = 1.77622                                                                        ν.sub.11 = 49.4                             r.sub.21 = -112.964                                                                       d.sub.21 = 6.70                                                     r.sub.22 = 0.000                                                                          d.sub.22 = 43.30                                                                         n.sub.12 = 1.51825                                                                        ν.sub.12 = 63.8                             r.sub.23 = 0.000                                                               ______________________________________                                         Aspheric coefficient                                                           ______________________________________                                         First surface:                                                                  K = 0.3664325    AD = 0.4574458 × 10.sup.-7                             AE = -0.3507965 × 10.sup.-10                                                               AF = 0.2388062 × 10.sup.-14                            AG = 0.2247566 × 10.sup.-19                                              Seventeenth surface:                                                            K = 0.1229070 × 10.sup.2                                                                   AD = 0.9272514 × 10.sup.-7                            AE = -0.3770400 × 10.sup.-10                                                               AF = 0.1428259 × 10.sup.-12                            AG = 0.5601794 × 10.sup.-16                                              Eighteenth surface:                                                             K = 0.2118076 × 10.sup.2                                                                  AD = -0.4127061 × 10.sup.-6                            AE = 0.2205876 × 10.sup.-9                                                                 AF = 0.6059036 × 10.sup.-13                            AG = 0.6235547 × 10.sup.-16                                              ______________________________________                                    

    ______________________________________                                         Sixth embodiment                                                               ______________________________________                                         f = 50.15           Aperture 1:2.8                                                                 ratio                                                      Projection 18.09    ω = 34.1°                                     magnification                                                                  f.sub.1.7 /f = 1.15 d.sub.15 /f = 0.67                                         d.sub.17 /f = 0.12  f.sub.8 /f.sub.9.10 = -1.33                                 r.sub.1 = 138.102                                                                         d.sub.1 = 8.40                                                                           n.sub.1 = 1.51825                                                                         ν.sub.1 = 63.8                                                                     *                                       r.sub.2 = 3278.162                                                                        d.sub.2 = 5.18                                                      r.sub.3 = 48.685                                                                          d.sub.3 = 6.00                                                                           n.sub.2 = 1.51825                                                                         ν.sub.2 = 63.8                              r.sub.4 = 29.654                                                                          d.sub.4 = 11.06                                                     r.sub.5 = 1869.065                                                                        d.sub.5 = 2.21                                                                           n.sub.3 = 1.52555                                                                         ν.sub.3 = 50.5                              r.sub.6 = 27.929                                                                          d.sub.6 = 18.76                                                     r.sub.7 = 74.902                                                                          d.sub.7 =  17.33                                                                         n.sub.4 = 1.85503                                                                         ν.sub.4 = 23.7                              r.sub.8 = -372.104                                                                        d.sub.8 = 6.68                                                      r.sub.9 = 271.686                                                                         d.sub.9 = 17.77                                                                          n.sub.5 = 1.79013                                                                         ν.sub.5 = 43.9                             r.sub.10 = -25.786                                                                        d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                         ν.sub.6 = 27.3                             r.sub.11 = 74.081                                                                         d.sub.11 = 4.62                                                     r.sub.12 = -81.511                                                                        d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                         ν.sub.7 = 49.4                             r.sub.13 = -43.199                                                                        d.sub.13 = 1.49                                                     r.sub.14 = 204.097                                                                        d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                         ν.sub.8 = 47.1                             r.sub.15 = -122.218                                                                       d.sub.15 = 33.60                                                    r.sub.16 = -45.791                                                                        d.sub.16 = 2.66                                                                           n.sub.9 =  ν.sub.9 = 36.4                             r.sub.17 = 288.771                                                                        d.sub.17 = 6.11              *                                      r.sub.18 = -339.448                                                                       d.sub.18 = 11.20                                                                         n.sub.10 = 1.68083                                                                        ν.sub.10 = 55.1                             r.sub.19 = -52.879                                                                        d.sub.19 = 0.25                                                     r.sub.20 = 237.092                                                                        d.sub.20 = 11.05                                                                         n.sub.11 = 1.77622                                                                        ν.sub.11 = 49.4                                                                     *                                      r.sub.21 = -107.581                                                                       d.sub.21 = 6.70                                                     r.sub.22 = 0.000                                                                          d.sub.22 = 43.30                                                                         n.sub.12 = 1.51825                                                                        ν.sub.12 = 63.8                             r.sub.23 = 0.000                                                               ______________________________________                                         Aspheric coefficient                                                           ______________________________________                                         First surface:                                                                  K = -0.8676696    AD = 0.4922937 × 10.sup.-7                            AE = -0.2681624 × 10.sup.-10                                                                AF = 0.4039305 × 10.sup.-14                           AG = -0.6315714 × 10.sup.-18                                             Seventeenth surface:                                                            K = 0.1204351 ×  10.sup.2                                                                  AD = 0.8134826 × 10.sup.-7                            AE = 0.3285905 × 10.sup.-11                                                                 AF = -0.3382158 × 10.sup.-13                          AG = 0.1685514 × 10.sup.-16                                              Twentieth surface:                                                              K = -0.1760054 × 10.sup.2                                                                  AD = -0.2229407 × 10.sup.-6                           AE = 0.8474120 × 10.sup.-10                                                                 AF = 0.3501296 × 10.sup.-13                           AG = -0.6162020 × 10.sup.-17                                             ______________________________________                                    

    ______________________________________                                         Seventh embodiment                                                             ______________________________________                                         f = 49.98           Aperture 1:2.8                                                                 ratio                                                      Projection 18.09    ω = 34.2°                                     magnification                                                                  f.sub.1.7 /f = 1.16 d.sub.15 /f = 0.67                                         d.sub.17 /f = 0.12  f.sub.8 /f.sub.9.10 = -1.35                                 r.sub.1 = 97.304                                                                          d.sub.1 = 8.40                                                                           n.sub.1 = 1.51825                                                                         ν.sub.1 = 63.8                              r.sub.2 = 419.135                                                                         d.sub.2 = 5.18                                                      r.sub.3 = 71.654                                                                          d.sub.3 = 6.00                                                                           n.sub.2 = 1.51825                                                                         ν.sub.2 = 63.8                              r.sub.4 = 34.797                                                                          d.sub.4 = 7.04                                                      r.sub.5 = 373.100                                                                         d.sub.5 = 2.21                                                                           n.sub.3 = 1.52555                                                                         ν.sub.3 = 50.5                              r.sub.6 = 27.138                                                                          d.sub.6 = 18.76                                                     r.sub.7 = 74.902                                                                          d.sub.7 =  17.33                                                                         n.sub.4 = 1.85503                                                                         ν.sub.4 = 23.7                              r.sub.8 = -372.104                                                                        d.sub.8 = 6.68                                                      r.sub.9 = 271.686                                                                         d.sub.9 = 17.77                                                                          n.sub.5 = 1.79013                                                                         ν.sub.5 = 43.9                             r.sub.10 = -25.786                                                                        d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                         ν.sub.6 = 27.3                             r.sub.11 = 74.081                                                                         d.sub.11 = 4.62                                                     r.sub.12 = -81.511                                                                        d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                         ν.sub.7 = 49.4                             r.sub.13 = -43.199                                                                        d.sub.13 = 1.49                                                     r.sub.14 = 204.097                                                                        d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                         ν.sub.8 = 47.1                             r.sub.15 = -122.218                                                                       d.sub.15 = 33.60                                                    r.sub.16 = -47.158                                                                        d.sub.16 = 2.66                                                                           n.sub.9 =  ν.sub.9 = 36.4                             r.sub.17 = 234.453                                                                        d.sub.17 = 6.11              *                                      r.sub.18 = -282.754                                                                       d.sub.18 = 10.70                                                                         n.sub.10 = 1.68083                                                                        ν.sub.10 = 55.1                                                                     *                                      r.sub.19 = -50.375                                                                        d.sub.19 = 0.25                                                     r.sub.20 = 387.424                                                                        d.sub.20 = 11.05                                                                         n.sub.11 = 1.77622                                                                        ν.sub.11 = 49.4                                                                     *                                      r.sub.21 = -89.653                                                                        d.sub.21 = 6.70                                                     r.sub.22 = 0.000                                                                          d.sub.22 = 43.30                                                                         n.sub.12 = 1.51825                                                                        ν.sub.12 = 63.8                             r.sub.23 = 0.000                                                               ______________________________________                                         Aspheric coefficient                                                           ______________________________________                                         Seventeenth surface:                                                            K = 0.3064228 × 10.sup.2                                                                  AD = 0.3424168 × 10.sup.-6                             AE = 0.1524318 × 10.sup.-11                                                                AF = 0.2578158 × 10.sup.-14                            AG = -0.1657459 × 10.sup.-16                                             Eighteenth surface:                                                             K =  -0.1540423 × 10.sup.2                                                                AD = -0.1423166 × 10.sup.-6                            AE = 0.2421751 × 10.sup.-9                                                                 AF = 0.9010286 × 10.sup.-13                            AG = 0.6174771 × 10.sup.-16                                              Twentieth surface:                                                              K = -0.1023903 × 10.sup.3                                                                 AD = -0.2301108 × 10.sup.-6                            AE = 0.1076672 × 10.sup.-9                                                                 AF = -0.1514403 × 10.sup.-14                           AG = -0.3385086 × 10.sup.-17                                             ______________________________________                                    

    ______________________________________                                         Eighth embodiment                                                              f = 50.09           Aperture 1:2.8                                                                 ratio                                                      Projection 18.09    ω = 34.1°                                     magnification                                                                  f.sub.1.7 /f = 1.13 d.sub.15 /f = 0.67                                         d.sub.17 /f = 0.12  f.sub.8 /f.sub.9.10 = -1.34                                ______________________________________                                         r.sub.1 =                                                                             100.392 d.sub.1 =                                                                              8.40                                                                               n.sub.1 = 1.51825                                                                       ν.sub.1 = 63.8                                                                      *                                  r.sub.2 =                                                                             203.275 d.sub.2 =                                                                              5.18                                                    r.sub.3 =                                                                              39.627 d.sub.3 =                                                                              6.00                                                                               n.sub.2 = 1.51825                                                                       ν.sub.2 = 63.8                          r.sub.4 =                                                                              24.889 d.sub.4 =                                                                             12.47                                                    r.sub.5 =                                                                             566.809 d.sub.5 =                                                                              2.21                                                                               n.sub.3 = 1.52555                                                                       ν.sub.3 = 50.5                          r.sub.6 =                                                                              29.209 d.sub.6 =                                                                             18.76                                                    r.sub.7 =                                                                              74.902 d.sub.7 =                                                                             17.33                                                                               n.sub. 4 = 1.85503                                                                      ν.sub.4 = 23.7                          r.sub.8 =                                                                            -372.104 d.sub.8 =                                                                              6.68                                                    r.sub.9 =                                                                             271.686 d.sub.9 =                                                                             17.77                                                                               n.sub.5 = 1.79013                                                                       ν.sub.5 = 43.9                          r.sub.10 =                                                                            -25.786 d.sub.10 =                                                                             2.00                                                                               n.sub.6 = 1.76169                                                                       ν.sub.6 = 27.3                          r.sub.11 =                                                                             74.081 d.sub.11 =                                                                             4.62                                                    r.sub.12 =                                                                            -81.511 d.sub.12 =                                                                             4.50                                                                               n.sub.7 = 1.77622                                                                       ν.sub.7 = 49.4                          r.sub.13 =                                                                            -43.199 d.sub.13 =                                                                             1.49                                                    r.sub.14 =                                                                            204.097 d.sub.14 =                                                                             4.11                                                                               n.sub.8 = 1.79196                                                                       ν.sub.8 = 47.1                          r.sub.15 =                                                                           -122.218 d.sub.15 =                                                                            35.89                                                    r.sub.16 =                                                                            -49.808 d.sub.16 =                                                                             2.66                                                                               n.sub.9 = 1.62059                                                                       ν .sub.9 = 36.4                         r.sub.17 =                                                                            275.553 d.sub.17 =                                                                             6.11                 *                                  r.sub.18 =                                                                           -519.026 d.sub.18 =                                                                            10.70                                                                               n.sub.10 = 1.68083                                                                      ν.sub.10 = 55.1                         r.sub.19 =                                                                            -60.159 d.sub.19 =                                                                             0.25                                                    r.sub.20 =                                                                            250.814 d.sub.20 =                                                                            11.05                                                                               n.sub.11 = 1.77622                                                                      ν.sub.11 = 49.4                         r.sub.21 =                                                                           -108.683 d.sub.21 =                                                                             6.70                                                    r.sub.22 =                                                                             0.000  d.sub.22 =                                                                            43.30                                                                               n.sub.12 = 1.51825                                                                      ν.sub.12 = 63.8                         r.sub.23 =                                                                             0.000                                                                  ______________________________________                                         Aspheric coefficient                                                           First surface:                                                                 K =     0.9525501     AD = 0.2216984 × 10.sup.-6                         AE =   -0.4500812 × 10.sup.-10                                                                 AF = 0.1270679 × 10.sup.-13                        AG =   -0.2481052 × 10.sup.-17                                           Seventeenth surface:                                                           K =     0.3154613 × 10.sup.2                                                                   AD = 0.5889586 × 10.sup.-6                         AE =   -0.5654111 × 10.sup.-9                                                                  AF = 0.5498361 × 10.sup.-13                        AG =    0.2775640 × 10.sup.-16                                           ______________________________________                                    

    ______________________________________                                         Ninth embodiment                                                               f = 49.91           Aperture 1:2.8                                                                 ratio                                                      Projection 18.07    ω = 34.2°                                     magnification                                                                  f.sub.1.7 /f = 1.13 d.sub.15 /f = 0.67                                         d.sub.17 /f = 0.12  f.sub.8 /f.sub.9.10 = -1.39                                ______________________________________                                         r.sub.1 =                                                                              92.116 d.sub.1 =                                                                              8.40                                                                               n.sub.1 = 1.51825                                                                       ν.sub.1 = 63.8                                                                      *                                  r.sub.2 =                                                                             256.167 d.sub.2 =                                                                              5.18                                                    r.sub.3 =                                                                              60.670 d.sub.3 =                                                                              6.00                                                                               n.sub.2 = 1.51825                                                                       ν.sub.2 = 63.8                          r.sub.4 =                                                                              29.056 d.sub.4 =                                                                              8.80                                                    r.sub.5 =                                                                             222.628 d.sub.5 =                                                                              2.21                                                                               n.sub.3 = 1.52555                                                                       ν.sub.3 = 50.5                          r.sub.6 =                                                                              28.187 d.sub.6 =                                                                             18.76                                                    r.sub.7 =                                                                               74.902                                                                               d.sub.7 =                                                                             17.33                                                                               n.sub.4 = 1.85503                                                                       ν.sub.4 = 23.7                          r.sub.8 =                                                                            -372.104 d.sub.8 =                                                                              6.68                                                    r.sub.9 =                                                                             271.686 d.sub.9 =                                                                             17.77                                                                               n.sub.5 = 1.79013                                                                       ν.sub.5 = 43.9                          r.sub.10 =                                                                            -25.786 d.sub.10 =                                                                             2.00                                                                               n.sub.6 = 1.76169                                                                       ν.sub.6 = 27.3                          r.sub.11 =                                                                             74.081 d.sub.11 =                                                                             4.62                                                    r.sub.12 =                                                                            -81.511 d.sub.12 =                                                                             4.50                                                                               n.sub.7 = 1.77622                                                                       ν.sub.7 = 49.4                          r.sub.13 =                                                                            -43.199 d.sub.13 =                                                                             1.49                                                    r.sub.14 =                                                                            204.097 d.sub.14 =                                                                             4.11                                                                               n.sub.8 = 1.79196                                                                       ν.sub.8 = 47.1                          r.sub.15 =                                                                           -122.218 d.sub.15 =                                                                            35.89                                                    r.sub.16 =                                                                            -55.629 d.sub.16  =                                                                            2.66                                                                               n.sub.9 = 1.62059                                                                       ν.sub.9 = 36.4                          r.sub.17 =                                                                            243.662 d.sub.17 =                                                                             6.11                                                    r.sub.18 =                                                                           -319.338 d.sub.18 =                                                                            10.70                                                                               n.sub.10 = 1.68083                                                                      ν.sub.10 = 55.1                                                                     *                                  r.sub.19 =                                                                            -61.756 d.sub.19 =                                                                             0.25                                                    r.sub.20 =                                                                            302.607 d.sub.20 =                                                                            11.05                                                                               n.sub.11 = 1.77622                                                                      ν.sub.11 = 49.4                         r.sub.21 =                                                                            -96.776 d.sub.21 =                                                                             6.70                                                    r.sub.22 =                                                                             0.000  d.sub.22 =                                                                            43.30                                                                               n.sub.12 = 1.51825                                                                      ν.sub.12 = 63.8                         r.sub.23 =                                                                             0.000                                                                  ______________________________________                                         Aspheric coefficient                                                           First surface:                                                                 K =     0.3399632     AD =     0.7523389 × 10.sup.-7                     AE =   -0.6005325 × 10.sup.-10                                                                 AF =     0.2647887 × 10.sup.-13                    AG =   - 0.5935675 × 10.sup.-17                                          Eighteenth surface:                                                            K =     0.2756654 × 10.sup.2                                                                   AD =    -0.7554289 × 10.sup.-6                     AE =    0.3478933 × 10.sup.-9                                                                  AF =    -0.7082334 × 10.sup.-13                    AG =    0.2544740 × 10.sup.-16                                           ______________________________________                                    

    ______________________________________                                         Tenth embodiment                                                               f = 50.04           Aperture 1:2.8                                                                 ratio                                                      Projection 18.10    ω = 34.2°                                     magnification                                                                  f.sub.1.7 /f = 1.14 d.sub.15 /f = 0.67                                         d.sub.17 /f = 0.12  f.sub.8 /f.sub.1.10 = -1.31                                ______________________________________                                         r.sub.1 =                                                                             114.457 d.sub.1 =                                                                              8.40                                                                               n.sub.1 = 1.51825                                                                       ν.sub.1 = 63.8                                                                      *                                  r.sub.2 =                                                                             483.920 d.sub.2 =                                                                              5.18                                                    r.sub.3 =                                                                              48.101 d.sub.3 =                                                                              6.00                                                                               n.sub.2 = 1.51825                                                                       ν.sub.2 = 63.8                          r.sub.4 =                                                                              28.146 d.sub.4 =                                                                              9.91                                                    r.sub.5 =                                                                             575.308 d.sub.5 =                                                                              2.21                                                                               n.sub.3 = 1.52555                                                                       ν.sub.3 = 50.5                          r.sub.6 =                                                                              28.386 d.sub.6 =                                                                             18.76                                                    r.sub.7 =                                                                               74.902                                                                               d.sub.7 =                                                                             17.33                                                                               n.sub.4 = 1.85503                                                                       ν.sub.4 = 23.7                          r.sub.8 =                                                                            -372.104 d.sub.8 =                                                                              6.68                                                    r.sub.9 =                                                                             271.686 d.sub.9 =                                                                             17.77                                                                               n.sub.5 = 1.79013                                                                       ν.sub.5 = 43.9                          r.sub.10 =                                                                            -25.786 d.sub.10 =                                                                             2.00                                                                               n.sub.6 = 1.76169                                                                       ν.sub.6 = 27.3                          r.sub.11 =                                                                             74.081 d.sub.11 =                                                                             4.62                                                    r.sub.12 =                                                                            -81.511 d.sub.12 =                                                                             4.50                                                                               n.sub.7 = 1.77622                                                                       ν.sub.7 = 49.4                          r.sub.13 =                                                                            -43.199 d.sub.13 =                                                                             1.49                                                    r.sub.14 =                                                                            204.097 d.sub.14 =                                                                             4.11                                                                               n.sub.8 = 1.79196                                                                       ν.sub.8 = 47.1                          r.sub.15 =                                                                           -122.218 d.sub.15 =                                                                            33.60                                                    r.sub.16 =                                                                            -46.081 d.sub.16 =                                                                             2.66                                                                               n.sub.9 = 1.62059                                                                       ν.sub.9 = 36.4                          r.sub.17 =                                                                            228.576 d.sub.17 =                                                                             6.11                                                    r.sub.18 =                                                                           -509.475 d.sub.18 =                                                                            10.70                                                                               n.sub.10 = 1.68083                                                                      ν.sub.10 = 55.1                         r.sub.19 =                                                                            -54.905 d.sub.19 =                                                                             0.25                                                    r.sub.20 =                                                                            238.750 d.sub.20 =                                                                            11.05                                                                               n.sub.11 = 1.77622                                                                      ν.sub.11 = 49.4                                                                     *                                  r.sub.21 =                                                                           -103.160 d.sub.21 =                                                                             6.70                                                    r.sub.22 =                                                                             0.000  d.sub.22 =                                                                            43.30                                                                               n.sub.12 = 1.51825                                                                      ν.sub.12 = 63.8                         r.sub.23 =                                                                             0.000                                                                  ______________________________________                                         Aspheric coefficient                                                           First surface:                                                                 K =     0.7070278     AD =     0.1345127 × 10.sup.-7                     AE =   -0.3754727 × 10.sup.-10                                                                 AF =     0.6046046 × 10.sup.-14                    AG =   -0.1657469 ×  10.sup.-17                                          Twentieth surface:                                                             K =    -0.1850460 × 10.sup.2                                                                   AD =    -0.2560358 × 10.sup.-6                     AE =    0.6946116 × 10.sup.-10                                                                 AF =     0.3196880 × 10.sup.-13                    AG =   -0.5231959 × 10.sup.-17                                           ______________________________________                                    

In the above embodiment, the radius of curvature values 0.000 represent flat surfaces. FIGS. 2 (a), (b), (c) to 11 (a), (b), (c) are characteristic graphs of the spheric aberrations, astigmatism aberrations, and distortion aberrations of the first to tenth embodiments. As is obvious from the characteristic graphs, each aberration is fairly compensated, and the high quality characteristics of images are realized.

In each of the above embodiments, the reflection type liquid crystal element is used as the image display element. However, the present invention is not to limited to the reflection type liquid crystal element, and can be replaced, as described earlier, by the image display devices, which form images as changed of transmittance and reflectivity by means of electric signals making use of birefringence and rotatory polarization characteristics electro optical crystal, PLZT, and so on.

FIG. 12 is a schematic view of the transmission type projection television system using the light source 9, the reflection type liquid crystal element 5 as the image display device having the angle-of-view dependency, and the projection lens 3, which has the telecentric characteristics, of the present invention. A bundle of image rays is magnified and projected on the screen 6 through the polarizing beam splitter 4 by means of the projection lens 3 of the present invention. A mirror 8 is used for bending route of the projection light for the purpose of minimizing the size of the housing of the transmission type projection television system. The reflection type liquid crystal display element itself is smaller than the conventional CRT devices forming images, and the projection lens has the high quality characteristics of images and the characteristics of wide field angle, so that the unique transmission type projection television having both the high quality characteristics of images and the minimized size can be realized. 

What is claimed is:
 1. A projection lens for projecting on a screen a transmission or reflection light from an image display device which forms from a light emitted from a light source an image as changes of transmittance or reflectivity in response to an electric signal applied thereto, said projection lens comprising an inverted telephoto type front lens group at a screen side and rear lens group having a front focal point nearby an exit pupil of said front lens group, and having telecentric characteristics, wherein the front lens group includes seven lenses, and the rear lens group includes three lenses, and wherein said projection lens meets the following condition:

    0.8<f.sub.1,7 /f<1.4

where f₁,7 : a total focal length of the front lens group, namely the first to seventh lenses f: a total focal length of the entire system.
 2. A projection lens for projecting on a screen a transmission or reflection light from an image display device which forms form a light emitted from a light source an image as changes of transmittance or reflectivity in response to an electric signal applied thereto, said projection lens comprising an inverted telephoto type front lens group at a screen side and a rear lens group having a front focal point nearby an exit pupil of said front lens group, and having telecentric characteristics, wherein the front lens group includes seven lenses, and the rear lens group includes three lenses, and wherein starting from the screen side, a first lens is a positive lens, a second lens is a negative meniscus lens having its convex surface facing the screen side, a third lens is a negative meniscus lens having its convex surface facing the screen side, a fourth lens is a bi-convex lens, a fifth lens is a negative meniscus lens including a cemented surface and having its convex surface facing the screen side, a sixth lens is a positive meniscus lens having its concave surface facing the screen side, a seventh lens is a bi-convex lens, an eighth lens is a bi-concave lens, a ninth lens is a positive lens, and a tenth lens is a bi-convex lens.
 3. A projection lens according to claim 1 meeting the following conditions:

    0.5<k.sub.15 /f<0.9

when a distance between surfaces of the front and rear lens groups is given as d₁₅, and a total focal length of the entire system is given as f.
 4. A projection lens according to claim 2 meeting the following conditions:

    d.sub.17 /f<0.3

    -1.5<f.sub.8 /f.sub.9.10 <-1.2

when it is given that a distance between surfaces of the eighth and ninth is d₁₇, a focal length of the eighth lens is f₈, a total focal length of the ninth and tenth lens is f₉,10, and a total focal length of the entire system is f.
 5. A projection lens according to claim 2, satisfying substantially the following conditions:

    ______________________________________                                         f = 49.86           Aperture 1:2.8                                                                 ratio                                                      Projection 16.89    ω = 36.2°                                     magnification                                                                  f.sub.1.7 f = 1.08  d.sub.15 /f = 0.72                                         d.sub.17 /f = 0.12  f.sub.8 /f.sub.9.10 = -1.42                                ______________________________________                                         r.sub.1 =                                                                              136.783 d.sub.1 =                                                                              8.10                                                                               n.sub.1 = 1.51825                                                                         ν.sub.1 = 63.8                       r.sub.2 =                                                                              961.173 d.sub.2 =                                                                              5.18                                                   r.sub.3 =                                                                              69.975  d.sub.3 =                                                                              6.00                                                                               n.sub.2 = 1.51825                                                                         ν.sub.2 = 63.8                       r.sub.4 =                                                                              27.036  d.sub.4 =                                                                              8.97                                                   r.sub.5 =                                                                              121.495 d.sub.5 =                                                                              2.21                                                                               n.sub.3 = 1.52555                                                                         ν.sub.3 = 50.5                       r.sub.6 =                                                                              29.715  d.sub.6 =                                                                             18.76                                                   r.sub.7 =                                                                              74.902  d.sub.7 =                                                                             17.33                                                                               n.sub.4 = 1.85503                                                                         ν.sub.4 = 23.7                       r.sub.8 =                                                                              327.104 d.sub.8 =                                                                              6.68                                                   r.sub.9 =                                                                              271.686 d.sub.9 =                                                                             17.77                                                                               n.sub.5 = 1.79013                                                                         ν.sub.5 = 43.9                       r.sub.10 =                                                                            -25.786  d.sub.10 =                                                                             2.00                                                                               n.sub.6 = 1.76169                                                                         ν.sub.6 = 27.3                       r.sub.11 =                                                                             74.081  d.sub.11 =                                                                             4.62                                                   r.sub.12 =                                                                            -81.511  d.sub.12 =                                                                             4.50                                                                               n.sub.7 = 1.77622                                                                         ν.sub.7 = 49.4                       r.sub.13 =                                                                             43.199  d.sub.13 =                                                                             1.49                                                   r.sub.14 =                                                                             204.097 d.sub.14 =                                                                             4.11                                                                               n.sub.8 = 1.79196                                                                         ν.sub.8 = 47.1                       r.sub.15 =                                                                            -122.218 d.sub.15 =                                                                            35.89                                                   r.sub.16 =                                                                            -68.864  d.sub.16  =                                                                            2.66                                                                               n.sub.9 = 1.61075                                                                         ν.sub.9 = 40.0                       r.sub.17 =                                                                             275.832 d.sub.17 =                                                                             6.11                                                   r.sub.18 =                                                                           -1075.96  d.sub.18 =                                                                            10.52                                                                               n.sub.10 = 1.68083                                                                        ν.sub.10 = 55.1                      r.sub.19 =                                                                            -88.713  d.sub.19 =                                                                             0.25                                                   r.sub.20 =                                                                             128.275 d.sub.20 =                                                                            10.01                                                                               n.sub.11 = 1.7762                                                                         ν.sub.11 = 49.4                      r.sub.21 =                                                                            -276.533 d.sub.21 =                                                                             4.70                                                   r.sub.22 =                                                                              0.000  d.sub.22 =                                                                            41.10                                                                               n.sub.12 = 1.51825                                                                        ν.sub.12 = 63.8                      r.sub.23 =                                                                              0.000                                                                 ______________________________________                                    

where r₁, r₂, . . . are a radius of curvature of each surface starting from the screen side, d₁, d₂, . . . are a distance between each of said surfaces, n₁, n₂, . . . are a refractive index at an e-line of each lens, and ν₁, ν₂, . . . are an Abbe's number corresponding to the e-line of each of the above lens.
 6. A projection lens according to claim 2, wherein at least one surface of the first, second, eighth, ninth and tenth lenses has an aspheric surface.
 7. A projection lens according to claim 6, satisfying substantially the following conditions:

    ______________________________________                                         f = 49.82           Aperture 1:2.8                                                                 ratio                                                      Projection 16.94    ω = 36.2°                                     magnification                                                                  f.sub.1.7 /f = 1.05 d.sub.15 /f = 0.74                                         d.sub.17 /f = 0.16  f.sub.8 /f.sub.9.10 = -1.33                                ______________________________________                                         r.sub.1 =                                                                             104.034 d.sub.1 =                                                                             11.00                                                                               n.sub.1 = 1.49384                                                                       ν.sub.1 = 57.4                                                                      *                                  r.sub.2 =                                                                             466.780 d.sub.2 =                                                                              5.00                 *                                  r.sub.3 =                                                                              73.295 d.sub.3 =                                                                              2.00                                                                               n.sub.2 = 1.49384                                                                       ν.sub.2 = 57.4                                                                      *                                  r.sub.4 =                                                                              26.295 d.sub.4 =                                                                             11.00                 *                                  r.sub.5 =                                                                             121.495 d.sub.5 =                                                                              2.21                                                                               n.sub.3 = 1.52555                                                                       ν.sub.3 = 50.5                          r.sub.6 =                                                                              29.715 d.sub.6 =                                                                             18.76                                                    r.sub.7 =                                                                               74.902                                                                               d.sub.7 =                                                                             17.33                                                                               n.sub.4 = 1.85503                                                                       ν.sub.4 = 23.7                          r.sub.8 =                                                                            -372.104 d.sub.8 =                                                                              6.68                                                    r.sub.9 =                                                                             271.686 d.sub.9 =                                                                             17.77                                                                               n.sub.5 = 1.79013                                                                       ν.sub.5 = 43.9                          r.sub.10 =                                                                            -25.786 d.sub.10 =                                                                             2.00                                                                               n.sub.6 = 1.76169                                                                       ν.sub.6 = 27.3                          r.sub.11 =                                                                             74.081 d.sub.11 =                                                                             4.62                                                    r.sub.12 =                                                                            -81.511 d.sub.12 =                                                                             4.50                                                                               n.sub.7 = 1.77622                                                                       ν.sub.7 = 49.4                          r.sub.13 =                                                                            -43.199 d.sub.13 =                                                                             1.49                                                    r.sub.14 =                                                                            204.097 d.sub.14 =                                                                             4.11                                                                               n.sub.8 = 1.79196                                                                       ν.sub.8 = 47.1                          r.sub.15 =                                                                           -122.218 d.sub.15 =                                                                            35.89                                                    r.sub.16 =                                                                            -62.109 d.sub.16  =                                                                            2.66                                                                               n.sub.9 = 1.61075                                                                       ν.sub.9 = 40.0                          r.sub.17 =                                                                            213.114 d.sub.17 =                                                                             7.80                                                    r.sub.18 =                                                                            847.406 d.sub.18 =                                                                            10.30                                                                               n.sub.10 = 1.68083                                                                      ν.sub.10 = 55.1                         r.sub.19 =                                                                            -95.951 d.sub.19 =                                                                             0.63                                                    r.sub.20 =                                                                            121.641 d.sub.20 =                                                                            10.45                                                                               n.sub.11 = 1.77622                                                                      ν.sub.11 = 49.4                         r.sub.21 =                                                                           -255.505 d.sub.21 =                                                                             4.50                                                    r.sub.22 =                                                                             0.000  d.sub.22 =                                                                            41.10                                                                               n.sub.12 = 1.51825                                                                      ν.sub.12 = 63.8                         r.sub.23 =                                                                             0.000                                                                  ______________________________________                                         Aspheric coefficient                                                           First surface:                                                                 K =     0.655275      AD =     0.626082 × 10.sup.-7                      AE =   -0.144786 × 10.sup.-10                                                                  AF =    -0.109334 × 10.sup.-14                     Second surface:                                                                K =     0.367907 × 10.sup.2                                              Third surface:                                                                 K =     0.440304      AD =     0.126898 × 10.sup.-7                      AE =    0.634832 × 10.sup.-11                                                                  AF =     0.928375 × 10.sup.-14                     Fourth surface:                                                                K =    -0.241861 × 10.sup.-1                                                                   AD =     0.166124 × 10.sup.-6                      AE =    0.434466 × 10.sup.-9                                                                   AF =     0.561828 × 10.sup.-12                     ______________________________________                                    

where r₁, r₂, . . . represent a radius of curvature of each surface starting from the screen side, d₁, d₂, . . . represent a distance between each of said surfaces, n₁, n₂, . . . represent a refractive index at an e-line of each lens, ν₁, ν₂, . . . represent an Abbe's number corresponding to the e-line of each of the above lens, surfaces represented by * . . . are the aspheric surfaces, and if Z is supposed a displacement amount from a vertex of a lens at a position away from an optical axis of the lens in a radius distance Y of an opening, it can be expressed as ##EQU2## and where AD, AE, AF, and AG are aspherical coefficients and K is a conical constant.
 8. A projection lens according to claim 6, satisfying substantially the following conditions:

    ______________________________________                                         f = 52.47           Aperture 1:2.8                                                                 ratio                                                      Projection 17.19    ω = 33.8°                                     magnification                                                                  f.sub.1.7 /f = 1.09 d .sub.15 /f = 0.64                                        d .sub.17 /f = 0.12 f .sub.8 /f.sub.9.10 = -1.31                               ______________________________________                                         r.sub.1 =                                                                              148.519 d.sub.1 =                                                                              8.40                                                                               n.sub.1 = 1.51825                                                                       ν.sub.1 = 63.8                                                                      *                                 r.sub.2 =                                                                            -6939.731 d.sub.2 =                                                                              5.18                                                   r.sub.3 =                                                                              49.137  d.sub.3 =                                                                              6.00                                                                               n.sub.2 = 1.51825                                                                       ν.sub.2 = 63.8                         r.sub.4 =                                                                              29.177  d.sub.4 =                                                                              9.37                 *                                 r.sub.5 =                                                                              608.860 d.sub.5 =                                                                              2.21                                                                               n.sub.3 = 1.52555                                                                       ν.sub.3 = 50.5                         r.sub.6 =                                                                              28.525  d.sub.6 =                                                                             18.76                                                   r.sub.7  =                                                                             74.902  d.sub.7 =                                                                             17.33                                                                               n.sub.4 = 1.85503                                                                       ν.sub.4 = 23.7                         r.sub.8 =                                                                             -372.104 d.sub.8 =                                                                              6.68                                                   r.sub.9 =                                                                              271.686 d.sub.9 =                                                                             17.77                                                                               n.sub.5 = 1.79013                                                                       ν.sub.5 = 43.9                         r.sub.10 =                                                                            -25.786  d.sub.10 =                                                                             2.00                                                                               n.sub.6 = 1.76169                                                                       ν.sub.6 = 27.3                         r.sub.11 =                                                                             74.081  d.sub.11 =                                                                             4.62                                                   r.sub.12 =                                                                            -81.511  d.sub.12 =                                                                             4.50                                                                               n.sub.7 = 1.77622                                                                       ν.sub.7 = 49.4                         r.sub.13 =                                                                            -43.199  d.sub.13 =                                                                             1.49                                                   r.sub.14 =                                                                             204.097 d.sub.14 =                                                                             4.11                                                                               n.sub.8 = 1.79196                                                                       ν.sub.8 = 47.1                         r.sub.15 =                                                                            -122.218 d.sub.15 =                                                                            33.60                                                   r.sub.16 =                                                                            -49.674  d.sub.16 =                                                                             2.66                                                                               n.sub.9 = 1.62059                                                                       ν.sub.9 = 36.4                         r.sub.17 =                                                                             298.959 d.sub.17 =                                                                             6.11                 *                                 r.sub.18 =                                                                            -275.028 d.sub.18 =                                                                            10.70                                                                               n.sub.10 = 1.68083                                                                      ν.sub.10 = 55.1                                                                     *                                 r.sub.19 =                                                                            -56.037  d.sub.19 =                                                                             0.25                                                   r.sub.20 =                                                                             341.327 d.sub.20 =                                                                            11.05                                                                               n.sub.11 = 1.77622                                                                      ν.sub.11 = 49.4                                                                     *                                 r.sub.21 =                                                                            -103.830 d.sub.21 =                                                                             6.70                                                   r.sub.22 =                                                                              0.000  d.sub.22 =                                                                            43.30                                                                               n.sub.12 = 1.51825                                                                      ν.sub.12 = 63.8                        r.sub.23 =                                                                              0.000                                                                 ______________________________________                                         Aspheric coefficient                                                           First surface:                                                                 K =    -0.2749912 × 10.sup.-1                                                                  AD =     0.2548179 × 10.sup.-7                     AE =   - 0.2056712 × 10.sup.-10                                                                AF =    -0.4319405 × 10.sup.-14                    AG =    0.8811238 × 10.sup.-18                                           Fourth surface:                                                                K =     0.3668809 × 10.sup.-1                                                                  AD =     0.1536691 × 10.sup.-6                     AE =   -0.1142634 × 10.sup.-10                                                                 AF =     0.8573753 × 10.sup.-12                    AG =    0.2158643 × 10.sup.-15                                           Seventeenth surface:                                                           K =     0.2637872 × 10.sup.2                                                                   AD =     0.1858271 × 10.sup.-6                     AE =    0.1334531 × 10.sup.-10                                                                 AF =     0.2612238 × 10.sup.-13                    AG =    0.9178511 × 10.sup.-17                                           Eighteenth surface:                                                            K =     0.5903051 × 10.sup.1                                                                   AD =    -0.2472130 × 10.sup.-6                     AE =    0.1460313 × 10.sup.-9                                                                  AF =     0.3400976 × 10.sup.-13                    AG =    0.3706282 × 10.sup.-17                                           Twentieth surface:                                                             K =    -0.9201606     AD =    -0.1022347 × 10.sup.-6                     AE =    0.7465995 × 10.sup.-10                                                                 AF =     0.1567219 × 10.sup.-13                    AG =    0.1032802 × 10.sup.-17                                           ______________________________________                                    

where r₁, r₂, . . . represent a radius of curvature of each surface starting from the screen side, d₁, d₂, represent a distance between each of said surfaces, n₁, n₂, . . . . . . represent a refractive index at an e-line of each lens, ν₁, ν₂, . . . represent an Abbe's number corresponding to the e-line of each of the above lens, surfaces represented by * . . . are the aspheric surfaces, and if Z is supposed a displacement amount from a vertex of a lens at a position away from an optical axis of the lens in radius distance Y of an opening, it can be expressed as ##EQU3## and where AD, AE, AF, and AG are aspherical coefficients, and K is a conical constant.
 9. A projection lens according to claim 6, satisfying substantially the following conditions:

    ______________________________________                                         f = 49.94           Aperture 1:2.8                                                                 ratio                                                      Projection 18.09                                                               magnification       ω = 34.1°                                     f.sub.1.7 /f =1.14  d.sub.15 /f = 0.67                                         d.sub.17 /f = 0.12  f.sub.8 /f.sub.9.10 = -1.37                                ______________________________________                                         r.sub.1 =                                                                             146.163 d.sub.1 =                                                                              8.40                                                                               n.sub.1 = 1.51825                                                                       ν.sub.1 = 63.8                                                                      *                                  r.sub.2 =                                                                              0.000  d.sub.2 =                                                                              5.18                                                    r.sub.3 =                                                                              49.670 d.sub.3 =                                                                              6.00                                                                               n.sub.2 = 1.51825                                                                       ν.sub.2 = 63.8                          r.sub.4 =                                                                              29.101 d.sub.4 =                                                                              9.39                 *                                  r.sub.5 =                                                                             937.536 d.sub.5 =                                                                              2.21                                                                               n.sub.3 = 1.52555                                                                       ν.sub.3 = 50.5                          r.sub.6 =                                                                              28.141 d.sub.6 =                                                                             18.76                                                    r.sub.7 =                                                                              74.902 d.sub.7 =                                                                             17.33                                                                               n.sub.4 = 1.85503                                                                       ν.sub.4 = 23.7                          r.sub.8 =                                                                            -372.104 d.sub.8 =                                                                              6.68                                                    r.sub.9 =                                                                             271.686 d.sub.9 =                                                                             17.77                                                                               n.sub.5 = 1.79013                                                                       ν.sub.5 = 43.9                          r.sub.10 =                                                                            -25.786 d.sub.10 =                                                                             2.00                                                                               n.sub.6 = 1.76169                                                                       ν.sub.6 = 27.3                          r.sub.11 =                                                                             74.081 d.sub.11 =                                                                             4.62                                                    r.sub.12 =                                                                            -81.511 d.sub.12 =                                                                             4.50                                                                               n.sub.7 = 1.77622                                                                       ν.sub.7 = 49.4                          r.sub.13 =                                                                            -43.199 d.sub.13 =                                                                             1.49                                                    r.sub.14 =                                                                            204.097 d.sub.14 =                                                                             4.11                                                                               n.sub.8 = 1.79196                                                                       ν.sub.8 = 47.1                          r.sub.15 =                                                                           -122.218 d.sub.15 =                                                                            33.60                                                    r.sub.16 =                                                                            -49.674 d.sub.16 =                                                                             2.66                                                                               n.sub.9 = 1.62059                                                                       ν.sub.9 = 36.4                          r.sub.17 =                                                                            303.305 d.sub.17 =                                                                             6.11                 *                                  r.sub.18 =                                                                           -310.381 d.sub.18 =                                                                            10.70                                                                               n.sub.10 = 1.68083                                                                      ν.sub.10 = 55.1                                                                     *                                  r.sub.19 =                                                                            -54.486 d.sub.19 =                                                                             0.25                                                    r.sub.20 =                                                                            275.356 d.sub.20 =                                                                            11.05                                                                               n.sub.11 = 1.77622                                                                      ν.sub.11 = 49.4                                                                     *                                  r.sub.21 =                                                                           -108.456 d.sub.21 =                                                                             6.70                                                    r.sub.22 =                                                                             0.000  d.sub.22 =                                                                            43.30                                                                               n.sub.12 = 1.51825                                                                      ν.sub.12 = 63.8                         r.sub.23 =                                                                             0.000                                                                  ______________________________________                                         Aspheric coefficient                                                           First surface:                                                                 K =    -0.2301050 × 10.sup.-1                                                                  AD =     0.2511178 × 10.sup.-7                     AE =   -0.1943356 × 10.sup.-10                                                                 AF =    -0.3619595 × 10.sup. -14                   AG =    0.8095271 × 10.sup.-18                                           Fourth surface:                                                                K =     0.3295092 × 10.sup.-1                                                                  AD =    -0.4594244 × 10.sup.-7                     AE =    0.7461787 × 10.sup.-10                                                                 AF =     0.4135199 × 10.sup.-12                    AG =   -0.3071122 × 10.sup.-15                                           Seventeenth surface:                                                           K =     0.2504243 × 10.sup.2                                                                   AD =     0.1782731 × 10.sup.-6                     AE =   -0.1529465 × 10.sup.-11                                                                 AF =     0.2164382 × 10.sup.-13                    AG =   -0.7725707 × 10.sup.-17                                           Eighteenth surface:                                                            K =     0.1032711 × 10.sup.-2                                                                  AD =    -0.2772488 × 10.sup.-6                     AE =    0.1544648 × 10.sup.-9                                                                  AF =     0.2193979 × 10.sup.-13                    AG =   -0.1042978 × 10.sup.-16                                           Twentieth surface:                                                             K =    -0.5525461 × 10.sup.1                                                                   AD =    -0.1231838 × 10.sup.-6                     AE =    0.8516421 × 10.sup.-10                                                                 AF =     0.1510178 × 10.sup.-13                    AG =    0.1229936 × 10.sup.-18                                           ______________________________________                                    

where r₁, r₂, . . . represent a radius of curvature of each surface starting from the screen side, d₁, d₂, . . . represent a distance between each of said surfaces, n₁, n₂, . . . represent a refractive index at an e-line of each lens, ν₁, ν₂, . . . represent an Abbe's number corresponding to the e-line of each of the above lens, surfaces represented by * . . . are the aspheric surfaces, and if Z is supposed a displacement amount from a vertex of a lens at a position away from an optical axis of the lens in a radius distance Y of an opening, it can be expressed as ##EQU4## and where AD, AE, AF, and AG are aspherical coefficients, and K is a conical constant.
 10. A projection lens according to claim 6, satisfying substantially the following conditions:

    ______________________________________                                         f = 50.00             Aperture      1:2.8                                                            ratio                                                    Projection   18.10    ω = 34.0°                                   magnification                                                                  f.sub.1.7 /f = 1.14   d.sub.15 /f = 0.67                                       d.sub.17 /f = 0.12    f.sub.8 /f.sub.9.10 = -1.35                              r.sub.1 = 139.093                                                                         d.sub.1 = 8.40                                                                            n.sub.1 = 1.51825                                                                          ν.sub.1 = 63.8*                           r.sub.2 = 1883.809                                                                        d.sub.2 = 5.18                                                      r.sub.3 = 44.322                                                                          d.sub.3 = 6.00                                                                            n.sub.2 = 1.51825                                                                          ν.sub.2 = 63.8                            r.sub.4 = 26.610                                                                          d.sub.4 = 11.06                                                     r.sub.5 = 1031.968                                                                        d.sub.5 = 2.21                                                                            n.sub.3 = 1.52555                                                                          ν.sub.3 = 50.5                            r.sub.6 = 28.804                                                                          d.sub.6 = 18.76                                                     r.sub.7 = 74.902                                                                          d.sub.7 = 17.33                                                                           n.sub.4 = 1.85503                                                                          ν.sub.4 = 23.7                            r.sub.8 = - 372.104                                                                       d.sub.8 = 6.68                                                      r.sub.9 = 271.686                                                                         d.sub.9 = 17.77                                                                           n.sub.5 = 1.79013                                                                          ν.sub.5 = 43.9                            r.sub.10 = -25.786                                                                        d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                          ν.sub.6 = 27.3                            r.sub.11 = 74.081                                                                         d.sub.11 = 4.62                                                     r.sub.12 = -81.511                                                                        d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                          ν.sub.7 = 49.4                            r.sub.13 = -43.199                                                                        d.sub.13 = 1.49                                                     r.sub.14 = 204.097                                                                        d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                          ν.sub.8 = 47.1                            r.sub.15 = -122.218                                                                       d.sub.15 = 33.60                                                    r.sub.16 = -48.652                                                                        d.sub.16 = 2.66                                                                           n.sub.9 = 1.62059                                                                          ν.sub.9 = 36.4                            r.sub.17 = 293.965                                                                        d.sub.17 = 6.11        *                                            r.sub.18 = -406.452                                                                       d.sub.18 = 10.70                                                                          n.sub.10 = 1.68083                                                                         ν.sub.10 = 55.1*                          r.sub.19 = -56.325                                                                        d.sub.19 = 0.25                                                     r.sub.20 = 243.391                                                                        d.sub.20 = 11.05                                                                          n.sub.11 = 1.77622                                                                         ν.sub.11 = 49.4                           r.sub.21 = -112.964                                                                       d.sub.21 = 6.70                                                     r.sub.22 = 0.000                                                                          d.sub.22 = 43.30                                                                          n.sub.12 = 1.51825                                                                         ν.sub.12 = 63.8                           r.sub.23 = 0.000                                                               Aspheric coefficient                                                           First surface:                                                                 K = 0.3664325      AD = 0.4574458 × 10.sup.-7                            AE = -0.3507965 × 10.sup.-10                                                                AF = 0.2388062 × 10.sup.-14                           AG = 0.2247566 × 10.sup.-19                                              Seventeenth surface:                                                           K = 0.1229070 × 10.sup.2                                                                    AD = 0.9272514 × 10.sup.-7                            AE = -0.3770400 × 10.sup.-10                                                                AF = 0.1428259 × 10.sup.-12                           AG = 0.5601794 × 10.sup.-16                                              Eighteenth surface:                                                            K =  0.2118076 × 10.sup.2                                                                   AD = -0.4127061 × 10.sup.-6                           AE = 0.2205876 × 10.sup.-9                                                                  AF = 0.6059036 × 10.sup.-13                           AG = 0.6235547 × 10.sup.-16                                              ______________________________________                                    

where r₁, r₂, . . . represent a radius of curvature of each surface starting from the screen side, d₁, d₂, . . . represent a distance between each of said surfaces, n₁, n₂, . . . represent a refractive index at an e-line of each lens, ν₁, ν₂, . . . represent an Abbe's number corresponding to the e-line of each of the above lens, surfaces represented by * . . . are the aspheric surfaces, and if Z is supposed a displacement amount from a vertex of a lens at a position away from an optical axis of the lens in a radius distance Y of an opening, it can be expressed as ##EQU5## and where AD, AE, AF, and AG are aspherical coefficients, and K is a conical constant.
 11. A projection lens according to claim 6, satisfying substantially the following conditions:

    ______________________________________                                         f = 50.15            Aperture       1:2.8                                                           ratio                                                     Projection  18.09    ω = 34.1°                                    magnification                                                                  f.sub.1.7 /f = 1.15  d.sub.15 /f = 0.67                                        d.sub.17 /f = 0.12   f.sub.8 /f.sub.9.10 = -1.33                               r.sub.1 = 138.102                                                                         d.sub.1 = 8.40                                                                            n.sub.1 = 1.51825                                                                          ν.sub.1 = 63.8*                           r.sub.2 = 3278.162                                                                        d.sub.2 = 5.18                                                      r.sub.3 = 48.685                                                                          d.sub.3 = 6.00                                                                            n.sub.2 = 1.51825                                                                          ν.sub.2 = 63.8                            r.sub.4 = 29.654                                                                          d.sub.4 = 11.06                                                     r.sub.5 = 1869.065                                                                        d.sub.5 = 2.21                                                                            n.sub.3 = 1.52555                                                                          ν.sub.3 = 50.5                            r.sub.6 = 27.929                                                                          d.sub.6 = 18.76                                                     r.sub.7 = 74.902                                                                          d.sub.7 = 17.33                                                                           n.sub.4 = 1.85503                                                                          ν.sub.4 = 23.7                            r.sub.8 = -372.104                                                                        d.sub.8 = 6.68                                                      r.sub.9 = 271.686                                                                         d.sub.9 = 17.77                                                                           n.sub.5 = 1.79013                                                                          ν.sub.5 = 43.9                            r.sub.10 = -25.786                                                                        d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                          ν.sub.6 = 27.3                            r.sub.11 = 74.081                                                                         d.sub.11 = 4.62                                                     r.sub.12 = -81.511                                                                        d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                          ν.sub.7 = 49.4                            r.sub.13 = -43.199                                                                        d.sub.13 = 1.49                                                     r.sub.14 = 204.097                                                                        d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                          ν.sub.8 = 47.1                            r.sub.15 = -122.218                                                                       d.sub.15 = 33.60                                                    r.sub.16 = -45.791                                                                        d.sub.16 = 2.66                                                                           n.sub.9 = 1.62059                                                                          ν.sub.9 = 36.4                            r.sub.17 = 288.771                                                                        d.sub.17 = 6.11        *                                            r.sub.18 = -339.448                                                                       d.sub.18 = 11.20                                                                          n.sub. 10 = 1.68083                                                                        ν.sub.10 = 55.1                           r.sub.19 = -52.879                                                                        d.sub.19 = 0.25                                                     r.sub.20 = 237.092                                                                        d.sub.20 = 11.05                                                                          n.sub.11 = 1.77622                                                                         ν.sub.11 = 49.4*                          r.sub.21 = -107.581                                                                       d.sub.21 = 6.70                                                     r.sub.22 = 0.000                                                                          d.sub.22 = 43.30                                                                          n.sub.12 = 1.51825                                                                         ν.sub.12 = 63.8                           r.sub.23 = 0.000                                                               Aspheric coefficient                                                           First surface:                                                                 K = -0.8676696    AD = 0.4922937 × 10.sup.-7                             AE = -0.2681624 × 10.sup.-10                                                               AF = 0.4039305 × 10.sup.-14                            AG = -0.6315714 × 10.sup.-18                                             Seventeenth surface:                                                           K = 0.1204351 × 10.sup.2                                                                   AD = 0.8134826 × 10.sup.-7                             AE = 0.3285905 × 10.sup.-11                                                                AF = -0.3382158 × 10.sup.-13                           AG = 0.1685514 × 10.sup.-16                                              Eighteenth surface:                                                            K =  -0.1760054 × 10.sup.2                                                                 AD = -0.2229407 × 10.sup.-6                            AE = 0.8474120 × 10.sup.-10                                                                AF = 0.3501296 × 10.sup.-13                            AG = -0.6162020 × 10.sup.-17                                             ______________________________________                                    

where r₁, r₂, . . . represent a radius of curvature of each surface starting from the screen side, d₁, d₂, . . . represent a distance between each of said surfaces, n₁, n₂, . . . represent a refractive index at an e-line of each lens, ν₁, ν₂, . . . represent an Abbe's number corresponding to the e-line of each of the above lens, surfaces represented by * . . . are the aspheric surfaces, and if Z is supposed a displacement amount from a vertex of a lens at a position away from an optical axis of the lens in a radius distance Y of an opening, it can be expressed as ##EQU6## and where AD, AE, AF, and AG are aspherical coefficients, and K is a conical constant.
 12. A projection lens according to claim 6, satisfying substantially the following conditions:

    ______________________________________                                         f = 49.98            Aperture       1:2.8                                                           ratio                                                     Projection  18.09    ω = 34.2°                                    magnification                                                                  f.sub.1.7 /f = 1.16  d.sub.15 /f = 0.67                                        d.sub.17 /f = 0.12   f.sub.8 /f.sub.9.10 = -1.33                               r.sub.1 = 97.304                                                                          d.sub.1 = 8.40                                                                            n.sub.1 = 1.51825                                                                          ν.sub.1 = 63.8                            r.sub.2 = 419.135                                                                         d.sub.2 = 5.18                                                      r.sub.3 = 71.654                                                                          d.sub.3 = 6.00                                                                            n.sub.2 = 1.51825                                                                          ν.sub.2 = 63.8                            r.sub.4 = 34.797                                                                          d.sub.4 = 7.04                                                      r.sub.5 = 373.100                                                                         d.sub.5 = 2.21                                                                            n.sub.3 = 1.52555                                                                          ν.sub.3 = 50.5                            r.sub.6 = 27.138                                                                          d.sub.6 = 18.76                                                     r.sub.7 = 74.902                                                                          d.sub.7 = 17.33                                                                           n.sub.4 = 1.85503                                                                          ν.sub.4 = 23.7                            r.sub.8 = - 372.104                                                                       d.sub.8 = 6.68                                                      r.sub.9 = 271.686                                                                         d.sub.9 = 17.77                                                                           n.sub.5 = 1.79013                                                                          ν.sub.5 = 43.9                            r.sub.10 = -25.786                                                                        d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                          ν.sub.6 = 27.3                            r.sub.11 = 74.081                                                                         d.sub.11 = 4.62                                                     r.sub.12 = -81.511                                                                        d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                          ν.sub.7 = 49.4                            r.sub.13 = -43.199                                                                        d.sub.13 = 1.49                                                     r.sub.14 = 204.097                                                                        d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                          ν.sub.8 = 47.1                            r.sub.15 = -122.218                                                                       d.sub.15 = 33.60                                                    r.sub.16 = -47.158                                                                        d.sub.16 = 2.66                                                                           n.sub.9 = 1.62059                                                                          ν.sub.9 = 36.4                            r.sub.17 = 234.453                                                                        d.sub.17 = 6.11        *                                            r.sub.18 = d.sub.18 = n.sub.10 = 1.68083                                                                         ν.sub.10 = 55.1*                          r.sub.19 = -50.375                                                                        d.sub.19 = 0.25                                                     r.sub.20 = 387.424                                                                        d.sub.20 = 11.05                                                                          n.sub.11 = 1.77622                                                                         ν.sub.11 = 49.4*                          r.sub.21 = -89.653                                                                        d.sub.21 = 6.70                                                     r.sub.22 = 0.000                                                                          d.sub.22 = 43.30                                                                          n.sub.12 = 1.51825                                                                         ν.sub.12 = 63.8                           r.sub.23 = 0.000                                                               Aspheric coefficient                                                           Seventeenth surface:                                                           K = 0.3064228 × 10.sup.2                                                                   AD = 0.3424168 × 10.sup.-6                             AE = 0.1524318 × 10.sup.-11                                                                AF = 0.2578158 × 10.sup.-14                            AG = -0.1657459 × 10.sup.-16                                             Eighteenth surface:                                                            K = -0.1540423 × 10.sup.2                                                                  AD = -0.1423166 × 10.sup.-6                            AE = 0.2421751 × 10.sup.-9                                                                 AF = 0.9010286 × 10.sup.-13                            AG = 0.6174771 × 10.sup.-16                                              Twentieth surface:                                                             K = -0.1023903 × 10.sup.3                                                                  AD = -0.2301108 × 10.sup.-6                            AE = 0.1076672 × 10.sup.-9                                                                 AF = -0.1514403 × 10.sup.-14                           AG = -0.3385086 × 10.sup.-17                                             ______________________________________                                    

where r₁, r₂, . . . represent a radius of curvature of each surface starting from the screen side, d₁, d₂, . . . represent a distance between each of said surfaces, n₁, n₂, . . . represent a refractive index at an e-line of each lens, ν₁, ν₂, . . . represent an Abbe's number corresponding to the e-line of each of the above lens, surfaces represented by * . . . are the aspheric surfaces, and if Z is supposed a displacement amount from a vertex of a lens at a position away from an optical axis of the lens in a radius distance Y of an opening, it can be expressed as ##EQU7## and where AD, AE, AF, and AG are aspherical coefficients, and K is a conical constant.
 13. A projection lens according to claim 6, satisfying substantially the following conditions:

    ______________________________________                                         f = 50.09             Aperture      1:2.8                                                            ratio                                                    Projection   18.09    ω = 34.1°                                   magnification                                                                  f.sub.1.7 /f = 1.13   d.sub.15 /f = 0.67                                       d.sub.17 /f = 0.12    f.sub.8 /f.sub.9.10 = -1.34                              r.sub.1 = 100.392                                                                         d.sub.1 = 8.40                                                                            n.sub.1 = 1.51825                                                                          ν.sub.1 = 63.8*                           r.sub.2 = 203.275                                                                         d.sub.2 = 5.18                                                      r.sub.3 = 39.627                                                                          d.sub.3 = 6.00                                                                            n.sub.2 = 1.51825                                                                          ν.sub.2 = 63.8                            r.sub.4 = 24.889                                                                          d.sub.4 = 12.47                                                     r.sub.5 = 566.809                                                                         d.sub.5 = 2.21                                                                            n.sub.3 = 1.52555                                                                          ν.sub.3 = 50.5                            r.sub.6 = 29.209                                                                          d.sub.6 = 18.76                                                     r.sub.7 = 74.902                                                                          d.sub.7 = 17.33                                                                           n.sub.4 = 1.85503                                                                          ν.sub.4 = 23.7                            r.sub.8 = - 372.104                                                                       d.sub.8 = 6.68                                                      r.sub.9 = 271.686                                                                         d.sub.9 = 17.77                                                                           n.sub.5 = 1.79013                                                                          ν.sub.5 = 43.9                            r.sub.10 = -25.786                                                                        d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                          ν.sub.6 = 27.3                            r.sub.11 = 74.081                                                                         d.sub.11 = 4.62                                                     r.sub.12 = -81.511                                                                        d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                          ν.sub.7 = 49.4                            r.sub.13 = -43.199                                                                        d.sub.13 = 1.49                                                     r.sub.14 = 204.097                                                                        d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                          ν.sub.8 = 47.1                            r.sub.15 = -122.218                                                                       d.sub.15 = 35.89                                                    r.sub.16 = -49.808                                                                        d.sub.16 = 2.66                                                                           n.sub.9 = 1.62059                                                                          ν.sub.9 = 36.4                            r.sub.17 = 275.553                                                                        d.sub.17 = 6.11        *                                            r.sub.18 = -519.026                                                                       d.sub.18 = 10.70                                                                          n.sub.10 = 1.68083                                                                         ν.sub.10 = 55.1                           r.sub.19 = -60.159                                                                        d.sub.19 = 0.25                                                     r.sub.20 = 250.814                                                                        d.sub.20 = 11.05                                                                          n.sub.11 = 1.77622                                                                         ν.sub.11 = 49.4                           r.sub.21 = -108.683                                                                       d.sub.21 = 6.70                                                     r.sub.22 = 0.000                                                                          d.sub.22 = 43.30                                                                          n.sub.12 = 1.51825                                                                         ν.sub.12 = 63.8                           r.sub.23 = 0.000                                                               Aspheric coefficient                                                           First surface:                                                                 K = 0.9525501      AD = 0.2216984 × 10.sup.-6                            AE = -0.4500812 × 10.sup.-10                                                                AF = 0.1270679 × 10.sup.-13                           AG = -0.2481052 × 10.sup.-17                                             Seventeenth surface:                                                           K = 0.3154613 × 10.sup.2                                                                    AD = 0.5889586 × 10.sup.-6                            AE = -0.5654111 × 10.sup.-9                                                                 AF = 0.5498361 × 10.sup.-13                           AG = 0.2775640 × 10.sup.-16                                              ______________________________________                                    

where r₁, r₂, . . . represent a radius of curvature of each surface starting from the screen side, d₁, d₂, . . . represent a distance between each of said surfaces, n₁, n₂, . . . represent a refractive index at an e-line of each lens, ν₁, ν₂, . . . represent an Abbe's number corresponding to the e-line of each of the above lens, surfaces represented by * . . . are the aspheric surfaces, and if Z is supposed a displacement amount from a vertex of a lens at a position away from an optical axis of the lens in a radius distance Y of an opening, it can be expressed as ##EQU8## and where AD, AE, AF, and AG are aspherical coefficients, and K is a conical constant.
 14. A projection lens according to claim 6, satisfying substantially the following conditions:

    ______________________________________                                         f = 49.91             Aperture      1:2.8                                                            ratio                                                    Projection   18.07    ω = 34.2°                                   magnification                                                                  f.sub.1.7 /f = 1.13   d.sub.15 /f = 0.67                                       d.sub.17 /f = 0.12    f.sub.8 /f.sub.9.10 = -1.39                              r.sub.1 = 92.116                                                                          d.sub.1 = 8.40                                                                            n.sub.1 = 1.51825                                                                          ν.sub.1 = 63.8*                           r.sub.2 = 256.167                                                                         d.sub.2 = 5.18                                                      r.sub.3 = 60.670                                                                          d.sub.3 = 6.00                                                                            n.sub.2 = 1.51825                                                                          ν.sub.2 = 63.8                            r.sub.4 = 29.056                                                                          d.sub.4 = 8.80                                                      r.sub.5 = 222.628                                                                         d.sub.5 = 2.21                                                                            n.sub.3 = 1.52555                                                                          ν.sub.3 = 50.5                            r.sub.6 = 28.187                                                                          d.sub.6 = 18.76                                                     r.sub.7 = 74.902                                                                          d.sub.7 = 17.33                                                                           n.sub.4 = 1.85503                                                                          ν.sub.4 = 23.7                            r.sub.8 = - 372.104                                                                       d.sub.8 = 6.68                                                      r.sub.9 = 271.686                                                                         d.sub.9 = 17.77                                                                           n.sub.5 = 1.79013                                                                          ν.sub.5 = 43.9                            r.sub.10 = -25.786                                                                        d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                          ν.sub.6 = 27.3                            r.sub.11 = 74.081                                                                         d.sub.11 = 4.62                                                     r.sub.12 = -81.511                                                                        d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                          ν.sub.7 = 49.4                            r.sub.13 = -43.199                                                                        d.sub.13 = 1.49                                                     r.sub.14 = 204.097                                                                        d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                          ν.sub.8 = 47.1                            r.sub.15 = -122.218                                                                       d.sub.15 = 35.89                                                    r.sub.16 = -55.629                                                                        d.sub.16 = 2.66                                                                           n.sub.9 = 1.62059                                                                          ν.sub.9 = 36.4                            r.sub.17 = 243.662                                                                        d.sub.17 = 6.11                                                     r.sub.18 = -319.338                                                                       d.sub.18 = 10.70                                                                          n.sub.10 = 1.68083                                                                         ν.sub.10 = 55.1*                          r.sub.19 = -61.756                                                                        d.sub.19 = 0.25                                                     r.sub.20 = 302.607                                                                        d.sub.20 = 11.05                                                                          n.sub.11 = 1.77622                                                                         ν.sub.11 = 49.4                           r.sub.21 = -96.776                                                                        d.sub.21 = 6.70                                                     r.sub.22 = 0.000                                                                          d.sub.22 = 43.30                                                                          n.sub.12 = 1.51825                                                                         ν.sub.12 = 63.8                           r.sub.23 = 0.000                                                               Aspheric coefficient                                                           First surface:                                                                 K = 0.3399632      AD = 0.7523389 × 10.sup.-7                            AE = -0.6005325 × 10.sup.-10                                                                AF = 0.2647887 × 10.sup.-13                           AG = -0.5935675 × 10.sup.-17                                             Eighteenth surface:                                                            K= 0.2756654 × 10.sup.2                                                                     AD = -0.7554289 × 10.sup.-6                           AE = 0.3478933 × 10.sup.-9                                                                  AF = -0.7082334 × 10.sup.-13                          AG = 0.2544740 × 10.sup.-16                                              ______________________________________                                    

where r₁, r₂, . . . represent a radius of curvature of each surface starting from the screen side, d₁, d₂, . . . represent a distance between each of said surfaces, n₁, n₂, . . . represent a refractive index at an e-line of each lens, ν₁, ν₂, . . . represent an Abbe's number corresponding to the e-line of each of the above lens, surfaces represented by * . . . are the aspheric surfaces, and if Z is supposed a displacement amount from a vertex of a lens at a position away from an optical axis of the lens in a radius distance Y of an opening, it can be expressed as ##EQU9## and where AD, AE, AF, and AG are aspherical coefficients, and K is a conical constant.
 15. A projection lens according to claim 6, satisfying substantially the following conditions:

    ______________________________________                                         f = 50.04             Aperture      1:2.8                                                            ratio                                                    Projection   18.10    ω = 34.2°                                   magnification                                                                  f.sub.1.7 /f = 1.14   d.sub.15 /f = 0.67                                       d.sub.17 /f = 0.12    f.sub.8 /f.sub.9.10 = -1.31                              r.sub.1 = 114.457                                                                         d.sub.1 = 8.40                                                                            n.sub.1 = 1.51825                                                                          ν.sub.1 = 63.8*                           r.sub.2 = 483.920                                                                         d.sub.2 = 5.18                                                      r.sub.3 = 48.101                                                                          d.sub.3 = 6.00                                                                            n.sub.2 = 1.51825                                                                          ν.sub.2 = 63.8                            r.sub.4 = 28.146                                                                          d.sub.4 = 9.91                                                      r.sub.5 = 575.308                                                                         d.sub.5 = 2.21                                                                            n.sub.3 = 1.52555                                                                          ν.sub.3 = 50.5                            r.sub.6 = 28.386                                                                          d.sub.6 = 18.76                                                     r.sub.7 = 74.902                                                                          d.sub.7 = 17.33                                                                           n.sub.4 = 1.85503                                                                          ν.sub.4 = 23.7                            r.sub.8 = - 372.104                                                                       d.sub.8 = 6.68                                                      r.sub.9 = 271.686                                                                         d.sub.9 = 17.77                                                                           n.sub.5 = 1.79013                                                                          ν.sub.5 = 43.9                            r.sub.10 = -25.786                                                                        d.sub.10 = 2.00                                                                           n.sub.6 = 1.76169                                                                          ν.sub.6 = 27.3                            r.sub.11 = 74.081                                                                         d.sub.11 = 4.62                                                     r.sub.12 = -81.511                                                                        d.sub.12 = 4.50                                                                           n.sub.7 = 1.77622                                                                          ν.sub.7 = 49.4                            r.sub.13 = -43.199                                                                        d.sub.13 = 1.49                                                     r.sub.14 = 204.097                                                                        d.sub.14 = 4.11                                                                           n.sub.8 = 1.79196                                                                          ν.sub.8 = 47.1                            r.sub.15 = -122.218                                                                       d.sub.15 = 33.60                                                    r.sub.16 = -46.081                                                                        d.sub.16 = 2.66                                                                           n.sub.9 = 1.62059                                                                          ν.sub.9 = 36.4                            r.sub.17 = 228.576                                                                        d.sub.17 = 6.11                                                     r.sub.18 = -509.475                                                                       d.sub.18 = 10.70                                                                          n.sub.10 = 1.68083                                                                         ν.sub.10 = 55.1                           r.sub.19 = -54.905                                                                        d.sub.19 = 0.25                                                     r.sub.20 = 238.750                                                                        d.sub.20 = 11.05                                                                          n.sub.11 = 1.77622                                                                         ν.sub.11 = 49.4*                          r.sub.21 = -103.160                                                                       d.sub.21 = 6.70                                                     r.sub.22 = 0.000                                                                          d.sub.22 = 43.30                                                                          n.sub.12 = 1.51825                                                                         ν.sub.12 = 63.8                           r.sub.23 = 0.000                                                               Aspheric coefficient                                                           First surface:                                                                 K = 0.7070278      AD = 0.1345127 × 10.sup.-7                            AE = -0.3754727 × 10.sup.-10                                                                AF = 0.6046046 × 10.sup.-14                           AG = -0.1657469 × 10.sup.-17                                             Twentieth surface:                                                             K= -0.1850460 × 10.sup.2                                                                    AD = -0.2560358 × 10.sup.-6                           AE = 0.6946116 × 10.sup.-10                                                                 AF = 0.3196880 × 10.sup.-13                           AG = -0.5231959 × 10.sup.-17                                             ______________________________________                                    

where r₁, r₂, . . . represent a radius of curvature of each surface starting from the screen side, d₁, d₂, . . . represent a distance between each of said surfaces, n₁, n₂, . . . represent a refractive index at an e-line of each lens, ν₁, ν₂, . . . represent an Abbe's number corresponding to the e-line of each of the above lens, surfaces represented by * . . . are the aspheric surfaces, and if Z is supposed a displacement amount from a vertex of a lens at a position away from an optical axis of the lens in a radius distance Y of an opening, it can be expressed as ##EQU10## and where AD, AE, AF, and AG are aspherical coefficients, and K is a conical constant.
 16. A projection lens for projecting on a screen a transmission or reflection light from an image display device which forms from a light emitted from a light source an image as changes of transmittance or reflectivity in response to an electric signal applied thereto, said projection lens comprising an inverted telephoto type front lens group at a screen side, and a rear lens group having a front focal point nearby an exit pupil of said front lens group, wherein said projection lens has telecentric characteristics and satisfies the following condition:

    0.8<f.sub.1 /f<1.4

where f₁ is a total focal length of the front lens group, and f is a total focal length of the entire system.
 17. A projection lens according to claim 16, satisfying the following condition:

    0.5<d.sub.15 /f<0.9

where d₁₅ is a distance between opposing surfaces of the front and rear lens group. 